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Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder

Sierra Ausin, Javier and Fabre, David and Citro, Vincenzo and Giannetti, Flavio Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder. (2020) Journal of Fluid Mechanics, 905 (A2). 1-25. ISSN 0022-1120

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Official URL: https://doi.org/10.1017/jfm.2020.692

Abstract

The aim of this paper is to provide a complete description of the bifurcation scenario of a uniform flow past a rotating circular cylinder up to Re=200 . Linear stability theory is used to depict the neutral curves and analyse the arising unstable global modes. Three codimension-two bifurcation points are identified, namely a Takens–Bogdanov, a cusp and generalised Hopf, which are closely related to qualitative changes in orbit dynamics. The occurrence of the cusp and Takens–Bogdanov bifurcations for very close parameters (corresponding to an imperfect codimension-three bifurcation) is shown to be responsible for the existence of multiple steady states, as already observed in previous studies. Two bistability regions are identified, the first with two stable fixed points and the second with a fixed point and a cycle. The presence of homoclinic and heteroclinic orbits, which are classical in the presence of Takens–Bogdanov bifurcations, is confirmed by direct numerical simulations. Finally, a weakly nonlinear analysis is performed in the neighbourhood of the generalised Hopf, showing that above this point the Hopf bifurcation is subcritical, leading to a third range of bistability characterised by both a stable fixed point and a stable cycle.

Item Type:Article
Additional Information:This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi:10.1017/jfm.2020.692
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Università degli Studi di Salerno - UniSa (ITALY)
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Deposited On:03 Jun 2021 07:41

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